Find the Roots (Zeros) f(x)=x^4+5x^2+4

Problem

ƒ(x)=x^4+5*x^2+4

Solution

1. Set the function to zero to find the roots of the polynomial.

x^4+5*x^2+4=0

2. Substitute a new variable to transform the equation into a quadratic form. Let u=x^2

u^2+5*u+4=0

3. Factor the quadratic equation by finding two numbers that multiply to 4 and add to 5

(u+1)*(u+4)=0

4. Solve for u by setting each factor equal to zero.

u=−1

u=−4

5. Back-substitute x^2 for u to solve for x

x^2=−1

x^2=−4

6. Apply the square root property to find the complex roots, using the identity √(,−1)=i

x=±√(,−1)=±i

x=±√(,−4)=±2*i

Final Answer

x=i,−i,2*i,−2*i

Want more problems? Check here!